As a conventional high-pressure fuel injection pipe for internal combustion engines such as in-cylinder injection type gasoline engines, there are known, for example, a fuel injection pipe for diesel engines, which is manufactured by repeating elongation and heat treatment of a thick-walled seamless steel pipe (material: STS35) (see JP-A-52-756), a fuel injection pipe for diesel engines, which is manufactured by repeating elongation and heat treatment of a thick-walled seamless stainless steel pipe (see JP-A-54-110958), and a welded pipe whose steel base is not exposed anywhere, made by forming, as a first plated layer, a plated layer of Ni, Co, or a base alloy thereof on at least one surface of a band steel sheet, forming, as a second plated layer on the first plated layer, a single metal or an alloy thereof having a lower melting point than the single metal of base alloy thereof of the first plated layer, using the band steel sheet formed with the two plated layers to fabricate an seam-welded pipe, and then performing heat treatment (see JP-A-5-9786). Further, there is known a welded pipe manufactured by forming a first plated layer composed of Sn, Sn—Zn, Sn—Ni, Ni—P, or Ni—B on at least one surface of a band steel sheet, forming, as a second plated layer on the first plated layer, Ni, Co, and one of the base metal alloys thereof which has a higher melting point than the metal forming the first plated layer, using the band steel sheet formed with the two plated layers to fabricate a pipe, and then performing heat treatment (see JP-A-5-156494).